Special Issue "Computational Mathematics and Mathematical Physics"

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 31 December 2023 | Viewed by 11684

Special Issue Editors

International Research Center on Mathematics and Mechanics of Complex Systems, University of L’Aquila, Via Giovanni Gronchi 18, 67100 L’Aquila, Italy
Interests: continuum mechanics; porous media; piezo-electro-mechanical structures; nonlinear elasticity; second gradient materials; metamaterials; mechanics of living tissue; smart materials; composite materials; experimental mechanics; numerical mechanics
Special Issues, Collections and Topics in MDPI journals
1. Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Moscow, Russia
2. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
Interests: partial differential equations & mathematical physics; elasticity system; stokes system; biharmonic (polyharmonic) equation
Special Issues, Collections and Topics in MDPI journals
Dipartimento di scienze Matematiche e Informatiche, scienze Fisiche e scienze della Terra dell'Università degli Studi di Messina Viale Ferdinando Stagno d'Alcontres, 31 - 98166 Messina, Italy
Interests: general topology; fibrewise topology; digital geometry; soft topology; neutrosophic topology

Special Issue Information

Dear Colleagues,

The main topics of this Special Issue are:

  • Discrete and Continuum Mechanics
    Metamaterials and smart structure designs, variational methods in mechanics, biomechanics, and experimental mechanics
  • Mathematical Physics and PDE
    Mathematical physics and PDE including fluid dynamics and the Helmhotz equation; solvability, regularity, stability, and other qualitative properties of linear and nonlinear equations and systems; scattering theory and inverse problems; variational methods and calculus of variations; dynamical systems
  • Topology, Computer Science, Digital Geometry, and Computational Geometry
  • Foundations of Mechanics, Postulations of Continuum Mechanics, and Variational Principles

Prof. Dr. Francesco dell’Isola
Prof. Dr. Hovik Matevossian
Prof. Dr. Giorgio Nordo
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • discrete and continuum mechanics, metamaterials and smart structure design, variational methods in mechanics, biomechanics, and experimental mechanics
  • mathematical physics, PDE, fluid dynamics, and applied mathematics
  • general and fiberwise general topology, digital geometry, soft topology, and neutrosophic topology

Published Papers (13 papers)

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Editorial

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Editorial
“Computational Mathematics and Mathematical Physics”—Editorial I (2021–2023)
Axioms 2023, 12(9), 824; https://doi.org/10.3390/axioms12090824 - 28 Aug 2023
Viewed by 264
Abstract
Based on the papers published in the Special Issue of the scientific journal Axioms, here we present the Editorial Article “Computational Mathematics and Mathematical Physics”, the main topics of which include both fundamental and applied research in computational mathematics and differential equations [...] Read more.
Based on the papers published in the Special Issue of the scientific journal Axioms, here we present the Editorial Article “Computational Mathematics and Mathematical Physics”, the main topics of which include both fundamental and applied research in computational mathematics and differential equations of mathematical physics [...] Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)

Research

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Article
Noninertial Proper Motions of the Minkowski Metric, the Sagnac Effect, and the Twin Paradox
Axioms 2023, 12(6), 537; https://doi.org/10.3390/axioms12060537 - 30 May 2023
Viewed by 434
Abstract
The Sagnac effect and related twin paradox with a rotating disc are analyzed. It may seem that the special theory of relativity gives an easy and exhaustive treatment here. However, such consideration is deceptive since the principles of special relativity are originally established [...] Read more.
The Sagnac effect and related twin paradox with a rotating disc are analyzed. It may seem that the special theory of relativity gives an easy and exhaustive treatment here. However, such consideration is deceptive since the principles of special relativity are originally established only for the inertial frames of reference, whereas the Sagnac experiment and the twin paradox exist in a noninertial one. We introduce an additional group of motions related to the rotation with uniform angular speed and show that these transformations leave the Minkowski metric invariant. Thus, we can give a firm mathematical ground to a usual easy consideration of the Sagnac effect. It should be noted that the presented result is true for a special case of motions; general coordinate transformations into accelerating frames of reference do not preserve the metric. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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Article
Existence and Qualitative Properties of Solution for a Class of Nonlinear Wave Equations with Delay Term and Variable-Exponents Nonlinearities
Axioms 2023, 12(5), 444; https://doi.org/10.3390/axioms12050444 - 30 Apr 2023
Viewed by 647
Abstract
This article is devoted to a study of the question of existence (in time) of weak solutions and the derivation of qualitative properties of such solutions for the nonlinear viscoelastic wave equation with variable exponents and minor damping terms. By using the energy [...] Read more.
This article is devoted to a study of the question of existence (in time) of weak solutions and the derivation of qualitative properties of such solutions for the nonlinear viscoelastic wave equation with variable exponents and minor damping terms. By using the energy method combined with the Faedo–Galerkin method, the local and global existence of solutions are established. Then, the stability estimate of the solution is obtained by introducing a suitable Lyapunov function. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
Article
Numerical Computation of Hybrid Morphologies of Nanoparticles on the Dynamic of Nanofluid: The Case of Blood-Based Fluid
Axioms 2023, 12(2), 163; https://doi.org/10.3390/axioms12020163 - 06 Feb 2023
Cited by 5 | Viewed by 889
Abstract
The movement of biological fluids in the human body is a premium field of interest to overcome growing biomedical challenges. Blood behavior shows different behavior in capillaries, veins, and arteries during circulation. In this paper, a new mathematical relation for the nano-layer of [...] Read more.
The movement of biological fluids in the human body is a premium field of interest to overcome growing biomedical challenges. Blood behavior shows different behavior in capillaries, veins, and arteries during circulation. In this paper, a new mathematical relation for the nano-layer of biological fluids flows with the effect of TiO2 and Ag hybrid nanoparticles was developed. Further, we explain the engineering phenomena of biological fluids and the role of hybrid nanoparticles in the blood vessel system. The improvement of drug delivery systems by using low seepage Reynolds number was associated with expansion/contraction and was discussed in detail through the rectangular domain. Using similarity transformation, the governing equations were converted into non-linear ordinary differential equations, and the mathematical problem was solved by employing the numerical shooting method. Plots of momentum, temperature, skin friction coefficient, as well as the Nusselt number on different non-dimensionless parameters are displayed via lower/upper porous walls of the channel. It was analyzed that the walls of the channel showed different results on magnetized physical parameters. Values of thermophoresis and the Brownian motion flow of the heat transfer rate gradually increased on the upper wall and decreased on the lower wall of the channel. The important thing is that the hybrid nanoparticles, rather than nano, were more useful for improving thermal conductivity, heat transfer rate, and the nano-layer. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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Article
Particles Dynamics in Schwarzschild like Black Hole with Time Contracting Horizon
Axioms 2023, 12(1), 34; https://doi.org/10.3390/axioms12010034 - 27 Dec 2022
Cited by 1 | Viewed by 854
Abstract
The black holes radiate their mass and energy in the form of gravitational waves and Hawking-radiation, which lead to a decrease in the mass and energy of the black holes. During the formation of gravitational waves and Hawking radiation, the mass and energy [...] Read more.
The black holes radiate their mass and energy in the form of gravitational waves and Hawking-radiation, which lead to a decrease in the mass and energy of the black holes. During the formation of gravitational waves and Hawking radiation, the mass and energy of black holes reduce continuously with the passage of time t. For this reason the metric tensor of the black hole should depends on time t. In this work, a time-dependent term is introduced in the horizon of black hole without losing its symmetry structure by using the approximate Noether symmetry equation. The time-dependent term affects the effective potential, effective force, and all the dynamic features of the black hole. They are discussed for neutral and charged particles. Profiles of the escape velocity of colliding particles are also taken into consideration. Lyapunov exponent is used to check the stability of the orbits of the black hole. Hawking temperature, Bekenstein entropy, Komar energy, and specific energy at horizon of the black hole are discussed in this scenario. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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Article
Tandem Recurrence Relations for Coefficients of Logarithmic Frobenius Series Solutions about Regular Singular Points
Axioms 2023, 12(1), 32; https://doi.org/10.3390/axioms12010032 - 27 Dec 2022
Viewed by 842
Abstract
We enhance Frobenius’ method for solving linear ordinary differential equations about regular singular points. Key to Frobenius’ approach is the exploration of the derivative with respect to a single parameter; this parameter is introduced through the powers of generalized power series. Extending this [...] Read more.
We enhance Frobenius’ method for solving linear ordinary differential equations about regular singular points. Key to Frobenius’ approach is the exploration of the derivative with respect to a single parameter; this parameter is introduced through the powers of generalized power series. Extending this approach, we discover that tandem recurrence relations can be derived. These relations render coefficients for series occurring in logarithmic solutions. The method applies to the, practically important, exceptional cases in which the roots of the indicial equation are equal, or differ by a non-zero integer. We demonstrate the method on Bessel’s equation and derive previously unknown tandem recurrence relations for coefficients of solutions of the second kind, for Bessel equations of all integer and half-integer order. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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Article
Six-Dimensional Space with Symmetric Signature and Some Properties of Elementary Particles
Axioms 2022, 11(11), 650; https://doi.org/10.3390/axioms11110650 - 17 Nov 2022
Viewed by 1009
Abstract
The six-dimensional pseudo-Euclidean space E3,3 with signature (3,3) is proposed as a model of real physical space at the subparticle scale. The conserved quantum characteristics of elementary particles, such as spin, isospin, electric and baryon charges, [...] Read more.
The six-dimensional pseudo-Euclidean space E3,3 with signature (3,3) is proposed as a model of real physical space at the subparticle scale. The conserved quantum characteristics of elementary particles, such as spin, isospin, electric and baryon charges, and hypercharge, are expressed through the symmetries of this space. The symmetries are brought out by the various representation of the metric in E3,3 with the aid of spinors and hyperbolic complex numbers. The properties of the metric allow predicting the number of quarks equal to 18. The violation of strong conservation laws in weak interactions is treated through compactifying the three-dimensional temporal subspace at the subparticle scale into single-dimensional time at bigger scales, which reduces symmetry from the spherical to axial type. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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Article
Global Existence of Bounded Solutions for Eyring–Powell Flow in a Semi-Infinite Rectangular Conduct
Axioms 2022, 11(11), 625; https://doi.org/10.3390/axioms11110625 - 08 Nov 2022
Cited by 1 | Viewed by 736
Abstract
The purpose of the present study is to obtain regularity results and existence topics regarding an Eyring–Powell fluid. The geometry under study is given by a semi-infinite conduct with a rectangular cross section of dimensions L×H. Starting from the initial [...] Read more.
The purpose of the present study is to obtain regularity results and existence topics regarding an Eyring–Powell fluid. The geometry under study is given by a semi-infinite conduct with a rectangular cross section of dimensions L×H. Starting from the initial velocity profiles (u10,u20) in xy-planes, the fluid flows along the z-axis subjected to a constant magnetic field and Dirichlet boundary conditions. The global existence is shown in different cases. First, the initial conditions are considered to be squared-integrable; this is the Lebesgue space (u10,u20)L2(Ω), Ω=[0,L]×[0,H]×(0,). Afterward, the results are extended for (u10,u20)Lp(Ω)p>2. Lastly, the existence criteria are obtained when (u10,u20)H1(Ω). A physical interpretation of the obtained bounds is provided, showing the rheological effects of shear thinningand shear thickening in Eyring–Powell fluids. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
Article
A Valid Quantization of the Particle in a Box Field Theory, and Well Beyond
Axioms 2022, 11(10), 567; https://doi.org/10.3390/axioms11100567 - 19 Oct 2022
Viewed by 695
Abstract
The usual particle in a box is turned into a field theory, and its behavior is examined using canonical and affine quantizations. The result leads to a valid affine quantization of the particle in a box field theory, which points toward further valid [...] Read more.
The usual particle in a box is turned into a field theory, and its behavior is examined using canonical and affine quantizations. The result leads to a valid affine quantization of the particle in a box field theory, which points toward further valid quantizations of more realistic field theory models. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
Article
Goodness-of-Fit Tests for Weighted Generalized Quasi-Lindley Distribution Using SRS and RSS with Applications to Real Data
Axioms 2022, 11(10), 490; https://doi.org/10.3390/axioms11100490 - 21 Sep 2022
Cited by 1 | Viewed by 780
Abstract
This paper deals with the problem of goodness-of-fit tests (GFTs) for the weighted generalized quasi-Lindley distribution (WGQLD) using ranked set sampling (RSS) and simple random sampling (SRS) techniques. The tests are based on the empirical distribution function and sample entropy. These tests include [...] Read more.
This paper deals with the problem of goodness-of-fit tests (GFTs) for the weighted generalized quasi-Lindley distribution (WGQLD) using ranked set sampling (RSS) and simple random sampling (SRS) techniques. The tests are based on the empirical distribution function and sample entropy. These tests include the Kullback–Leibler, Kolomogorov–Smirnov, Anderson–Darling, Cramér–von Mises, Zhang, Liao, and Shimokawa, and Watson tests. The critical values (CV) and power of each test are obtained based on a simulation study by using SRS and RSS methods considering various sample sizes and alternatives. A rain data set is used to investigate the effectiveness of the suggested GFTs. Based on the same number of measured units for the various alternatives taken into consideration in this study, it is discovered that the RSS tests are more effective than those of their rivals in SRS. Additionally, as the set size increases, the GFTs’ power increases. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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Article
Asymptotic Behavior of Solutions of the Cauchy Problem for a Hyperbolic Equation with Periodic Coefficients II
Axioms 2022, 11(9), 473; https://doi.org/10.3390/axioms11090473 - 16 Sep 2022
Cited by 2 | Viewed by 935
Abstract
The paper is devoted to studying the behavior of solutions of the Cauchy problem for large values of time—more precisely, obtaining an asymptotic expansion characterizing the behavior of the solution of the Cauchy problem for a one-dimensional second-order hyperbolic equation with periodic coefficients [...] Read more.
The paper is devoted to studying the behavior of solutions of the Cauchy problem for large values of time—more precisely, obtaining an asymptotic expansion characterizing the behavior of the solution of the Cauchy problem for a one-dimensional second-order hyperbolic equation with periodic coefficients for large values of the time parameter t. To obtain this asymptotic expansion as t→∞, methods of the spectral theory of differential operators are used, as well as the properties of the spectrum of a non-positive Hill operator with periodic coefficients. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
Article
Complex Dynamics Analysis of a Discrete Amensalism System with a Cover for the First Species
Axioms 2022, 11(8), 365; https://doi.org/10.3390/axioms11080365 - 26 Jul 2022
Cited by 4 | Viewed by 961
Abstract
Of interest is the dynamics of the discrete-time amensalism model with a cover on the first species. We first obtain the existence and stability of fixed points and the conditions for the permanent coexistence of two species. Then we demonstrate the occurrence of [...] Read more.
Of interest is the dynamics of the discrete-time amensalism model with a cover on the first species. We first obtain the existence and stability of fixed points and the conditions for the permanent coexistence of two species. Then we demonstrate the occurrence of flip bifurcation by using the central manifold theorem and bifurcation theory. A hybrid control strategy is used to control the flip bifurcation and stabilize unstable periodic orbits embedded in the complex attractor. Numerical simulation verifies the feasibility of theoretical analysis and reveals some novel and exciting dynamic phenomena. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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Article
A Valid Quantization of a Half-Harmonic Oscillator Field Theory
Axioms 2022, 11(8), 360; https://doi.org/10.3390/axioms11080360 - 24 Jul 2022
Cited by 1 | Viewed by 915
Abstract
The usual full- and half-harmonic oscillators are turned into field theories, and that behavior is examined using canonical and affine quantization. The result leads to a valid affine quantization of the half harmonic oscillator field theory, which points toward further valid quantizations of [...] Read more.
The usual full- and half-harmonic oscillators are turned into field theories, and that behavior is examined using canonical and affine quantization. The result leads to a valid affine quantization of the half harmonic oscillator field theory, which points toward further valid quantizations of more realistic field theory models. Full article
(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)
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